3NF

3NF (Third Normal Form) is a normalization level where a relation is already in 2NF and has no transitive functional dependencies. A table is in 3NF if:

• It is in 2NF (no partial dependencies).

• Every non-key attribute is non-transitively dependent on the primary key.

In simple terms, in 3NF, each non-key attribute should depend directly on the primary key, not through another non-key attribute.

What Is a Transitive Dependency?

A transitive dependency exists when:

X → Y and Y → Z

but X does not directly determine Z by itself.

Then:

X → Z

is said to be transitive through Y.

Example

Suppose a STUDENT table has:

Roll_No, Branch, HOD_Name

If:

Roll_No → Branch

Branch → HOD_Name

then:

Roll_No → HOD_Name

is a transitive dependency.

This is not allowed in 3NF.

How to Achieve 3NF

To bring a 2NF table into 3NF:

• Identify transitive dependencies (non-key attributes that determine other non-key attributes).

• Create new tables so that each non-key attribute depends only on the key.

Using the STUDENT example:

Original 2NF Table (with Transitive Dependency)

Here, Branch → HOD_Name, so HOD_Name transitively depends on Roll_No via Branch.

Split Into

BRANCH(Branch, HOD_Name)

STUDENT(Roll_No, Branch)

Now:

• In BRANCH, Branch → HOD_Name (direct, allowed).

• In STUDENT, non-key attribute Branch depends only on Roll_No.

Both tables are in 3NF.

Why 3NF Matters?

• It removes more redundancy (same HOD repeated for every student in a branch).

• It reduces update and deletion anomalies when the HOD changes.

• It is considered sufficient for most practical database designs.

Summary

3NF in DBMS requires a table to be in 2NF and to have no transitive dependencies: non-key attributes must depend only on the primary key, not on other non-key attributes. By splitting tables that contain transitive dependencies, 3NF further cleans up the design and improves data consistency, making it one of the most important normal forms for beginners.